Crash Course in Symbolic Logic

http://mathforum.org/dr.math/faq/symbolic_logic.html

Philosophers and Logicians

Logic Takes Small Steps
Shorthand Sentences
Connectives
Parentheses

Using Connectives

Subsentences

Complicated Sentences

What the Connectives Mean

The Rules of Logic
1. Assumptions
2. -> Introduction
3. ^ Elimination
4. Repetition
5. ^ Introduction
6. -> Elimination
7. <-> Introduction
8. <-> Elimination
9. ~ Introduction
10. ~ Elimination
11. v Introduction
12. v Elimination
Why These 12 Rules? A Review

Mundane Rules
repetition
^ introduction
^ elimination
-> elimination
<-> introduction
<-> elimination
v introduction
v elimination

Special Rule
assumptions

Fun Rules
-> introduction
~ introduction
~ elimination

Deriving a Conclusion

Deriving a Sentence

Rules with Latin Names
1. Modus Ponens
2. Modus Tollens
3. DeMorgan's Law (I)
4. DeMorgan's Law (II)
5. Hypothetical Syllogism
6. Disjunctive Syllogism
7. Reductio Ad Absurdum
8. Double Negation
9. Switcheroo
10. Disjunctive Addition
11. Simplification
12. Rule of Joining